Tangent Planes and Tangent Plane Approximations Illustration

This movie was created using Pacific Tech Graphing Calculator. Shows tangent plane to a surface z = f(x,y) at an animated point (a, b). It also shows the surface tangent vectors in the x- and y-directions whose cross-product yields the normal vector, also shown.

Finally, the exact point (a+∆x, b+∆y, f(a+∆x, b+∆y)) is shown along with and the corresponding tangent vector approximation point.